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Issue No.11 - Nov. (2012 vol.18)
pp: 1891-1901
M. Livesu , Dipt. di Mat. e Inf., Univ. degli Studi di Cagliari, Cagliari, Italy
F. Guggeri , Dipt. di Mat. e Inf., Univ. degli Studi di Cagliari, Cagliari, Italy
R. Scateni , Dipt. di Mat. e Inf., Univ. degli Studi di Cagliari, Cagliari, Italy
Curve-skeletons are the most important descriptors for shapes, capable of capturing in a synthetic manner the most relevant features. They are useful for many different applications: from shape matching and retrieval, to medical imaging, to animation. This has led, over the years, to the development of several different techniques for extraction, each trying to comply with specific goals. We propose a novel technique which stems from the intuition of reproducing what a human being does to deduce the shape of an object holding it in his or her hand and rotating. To accomplish this, we use the formal definitions of epipolar geometry and visual hull. We show how it is possible to infer the curve-skeleton of a broad class of 3D shapes, along with an estimation of the radii of the maximal inscribed balls, by gathering information about the medial axes of their projections on the image planes of the stereographic vision. It is definitely worth to point out that our method works indifferently on (even unoriented) polygonal meshes, voxel models, and point clouds. Moreover, it is insensitive to noise, pose-invariant, resolution-invariant, and robust when applied to incomplete data sets.
stereo image processing, computational geometry, image reconstruction, mesh generation, shape recognition, point clouds, curve-skeleton reconstruction, 3D shapes, visual hull, shape matching, shape retrieval, medical imaging, animation, epipolar geometry, maximal inscribed balls, medial projections axes, stereographic vision, polygonal meshes, voxel models, Shape, Skeleton, Cameras, Three dimensional displays, Humans, Visualization, Approximation methods, visual hull, Curve-skeleton, stereoscopic vision
M. Livesu, F. Guggeri, R. Scateni, "Reconstructing the Curve-Skeletons of 3D Shapes Using the Visual Hull", IEEE Transactions on Visualization & Computer Graphics, vol.18, no. 11, pp. 1891-1901, Nov. 2012, doi:10.1109/TVCG.2012.71
[1] H. Blum, "A Transformation for Extracting New Descriptions of Shape," Models for the Perception of Speech and Visual Form, pp. 362-380, MIT Press, 1967.
[2] T.K. Dey and J. Sun, "Defining and Computing Curve-Skeletons with Medial Geodesic Function," Proc. Eurographics Symp. Geometry Processing, pp. 143-152, 2006.
[3] D. Marr, "Analysis of Occluding Contour," Proc. Royal Soc. London. Series B, Biological Sciences, vol. 197, no. 1129, pp. 441-475, 1977.
[4] D. Hoffman and W. Richards, "Parts of Recognition," Cognition, vol. 18, nos. 1-3, pp. 65-96, 1984.
[5] D. Marr and H.K. Nishihara, "Representation and Recognition of the Spatial Organization of Three-Dimensional Shapes," Proc. Royal Soc. London. Series B, Biological Sciences, vol. 200, no. 1140, pp. 269-294, 1978.
[6] W.A. Richards, J.J. Koenderink, and D.D. Hoffman, "Inferring Three-Dimensional Shapes from Two-Dimensional Silhouettes," J. Optical Soc. Am., vol. A4, no. 7, pp. 1168-1175, July 1987.
[7] J.M.H. Beusmans, D.D. Hoffman, and B.M. Bennett, "Description of Solid Shape and Its Inference from Occluding Contours," J. Optical Soc. Am., vol. A4, no. 7, pp. 1155-1167, July 1987.
[8] E. Bullitt, A. Liu, and S. Pizer, "Three-Dimensional Reconstruction of Curves from Pairs of Projection Views in the Presence of Error (I. Algorithms)," Medical Physics, vol. 24, no. 24, pp. 1671-1678, 1997.
[9] S.M. Yoon, C. Malerczyk, and H. Graf, "3D Skeleton Extraction from Volume Data Based on Normalized Gradient Vector Flow," Proc. 17th Int'l Conf. Central Europe on Computer Graphics, Visualization and Computer Vision, pp. 177-182, 2009.
[10] S.M. Seitz and C.R. Dyer, "Photorealistic Scene Reconstruction by Voxel Coloring," Proc. IEEE CS Conf. Computer Vision and Pattern Recognition (CVPR '97), pp. 1067-1073, 1997.
[11] R.D. Murch and B.P. McGregor, "Reconstituting Object Shape and Orientation from Silhouettes," J. Optical Soc. Am., vol. A9, no. 9, pp. 1491-1497, Sept. 1992.
[12] E. Leek, "Effects of Stimulus Orientation on the Identification of Common Polyoriented Objects," Psychonomic Bull. and Rev., vol. 5, no. 4, pp. 650-658, 1998.
[13] N.D. Cornea, D. Silver, and P. Min, "Curve-Skeleton Applications," Proc. IEEE Visualization, pp. 95-102, Oct. 2005.
[14] X. Zhang, J. Liu, Z. Li, and M. Jaeger, "Volume Decomposition and Hierarchical Skeletonization," Proc. ACM SIGGRAPH Int'l Conf. Virtual-Reality Continuum and Its Applications in Industry (VRCAI '08), pp. 1-6, 2008.
[15] C.M. Ma and M. Sonka, "A Fully Parallel 3D Thinning Algorithm and Its Applications," Computer Vision Image Understanding, vol. 64, no. 3, pp. 420-433, 1996.
[16] T. Wang and A. Basu, "A Note on 'A Fully Parallel 3D Thinning Algorithm and Its Applications'," Pattern Recognition Letters, vol. 28, no. 4, pp. 501-506, 2007.
[17] N. Cornea, D. Silver, X. Yuan, and R. Balasubramanian, "Computing Hierarchical Curve-Skeletons of 3D Objects," The Visual Computer, vol. 21, no. 11, pp. 945-955, Oct. 2005.
[18] N. Gagvani and D. Silver, "Parameter-Controlled Volume Thinning," Graphical Models and Image Processing, vol. 61, no. 3, pp. 149-164, 1999.
[19] M.S. Hassouna and A.A. Farag, "Robust Centerline Extraction Framework Using Level Sets," Proc. IEEE CS Conf. Computer Vision and Pattern Recognition (CVPR '05), vol. 1, pp. 458-465, 2005.
[20] L. Liu, E.W. Chambers, D. Letscher, and T. Ju, "A Simple and Robust Thinning Algorithm on Cell Complexes," Computer Graphics Forum, vol. 29, no. 7, pp. 2253-2260, 2010.
[21] O.K.-C. Au, C.-L. Tai, H.-K. Chu, D. Cohen-Or, and T.-Y. Lee, "Skeleton Extraction by Mesh Contraction," Proc. SIGGRAPH '08, pp. 1-10, Aug. 2008.
[22] J. Cao, A. Tagliasacchi, M. Olson, H. Zhang, and Z. Su, "Point Cloud Skeletons via Laplacian Based Contraction," Proc. Shape Modeling Int'l Conf. (SMI '10), pp. 187-197, June 2010.
[23] A. Sharf, T. Lewiner, A. Shamir, and L. Kobbelt, "On-the-Fly Curve-Skeleton Computation for 3D Shapes," Computer Graphics Forum, vol. 26, no. 3, pp. 323-328, Oct. 2007.
[24] J.-M. Lien, J. Keyser, and N.M. Amato, "Simultaneous Shape Decomposition and Skeletonization," Proc. ACM Symp. Solid and Physical Modeling (SPM '06), pp. 219-228, 2006.
[25] A. Laurentini, "The Visual Hull Concept for Silhouette-Based Image Understanding," IEEE Trans. Pattern Analysis Machine Intelligence, vol. 16, no. 2, pp. 150-162, Feb. 1994.
[26] S. Petitjean, "A Computational Geometric Approach to Visual Hulls," Int'l J. Computational Geometry & Applications, vol. 8, pp. 407-436, 1998.
[27] G. Sanniti di Baja, "Well-Shaped, Stable, and Reversible Skeletons from the (3,4)-Distance Transform," J. Visual Comm. and Image Representation, vol. 5, pp. 107-115, 1994.
[28] P. Yim, P. Choyke, and R. Summers, "Gray-Scale Skeletonization of Small Vessels in Magnetic Resonance Angiography," IEEE Trans. Medical Imaging, vol. 19, no. 6, pp. 568-576, June 2000.
[29] L. Serino, G.S. di Baja, and C. Arcelli, "Object Decomposition via Curvilinear Skeleton Partition," Proc. Int'l Conf. Pattern Recognition (ICPR), pp. 4081-4084, 2010.
[30] A. Tagliasacchi, H. Zhang, and D. Cohen-Or, "Curve Skeleton Extraction from Incomplete Point Cloud," ACM Trans. Graphics, vol. 28, no. 3, pp. 1-9, 2009.
[31] B. Miklos, J. Giesen, and M. Pauly, "Discrete Scale Axis Representations for 3D Geometry," ACM Trans. Graphics, vol. 29, pp. 101:1-101:10, July 2010.
[32] A.P. Witkin, "Scale-Space Filtering," Proc. Eighth Int'l Joint Conf. Artificial Intelligence, vol. 2, pp. 1019-1022, 1983.
[33] H. Sundar, D. Silver, N. Gagvani, and S. Dickinson, "Skeleton Based Shape Matching and Retrieval," Proc. Shape Modeling Int'l Conf. (SMI '03), pp. 130-142, 2003.
[34] O.K.-C. Au, C.-L. Tai, D. Cohen-Or, Y. Zheng, and H. Fu, "Electors Voting for Fast Automatic Shape Correspondence," Computer Graphics Forum, vol. 29, no. 2, pp. 645-654, May 2010.
[35] P. Alliez, D. Cohen-Steiner, Y. Tong, and M. Desbrun, "Voronoi-Based Variational Reconstruction of Unoriented Point Sets," Proc. Fifth Eurographics Symp. Geometry Processing (SGP '07), pp. 39-48, July 2007.
[36] H. Sheung and C.C.L. Wang, "Robust Mesh Reconstruction from Unoriented Noisy Points," Proc. SIAM/ACM Joint Conf. Geometric and Physical Modeling (SPM '09), pp. 13-24, 2009.
[37] S.J. Shyu, T. Chou, and T.L. Chia, "Distance Transformation in Parallel," Proc. Workshop Combinatorial Math. and Computation Theory, pp. 298-304, 2006.
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